Any modulation method can be represented by a constellation. An example of this is the eight point constellation illustrated in FIG. 14. This constellation is generated from differentially encoded QPSK(DEQPSK or .pi./4 QPSK) which is a subset of the four state QPSK constellation. Each state is characterized by a vector having the same magnitude, but a different phase angle. In a Rayleigh faded channel, the constellation has continuous but slowly varying, with respect to the data rate, amplitude and phase modulation imposed on it. A coherent detector has the ability to track the phase modulation and cancel it, generating the original eight point constellation. Although the envelope or amplitude modulation still remains imposed on the signal, it is not a problem for data recovery since all the data information is contained in the phase shifts.
In a delay spread field, the channel has the same characteristics but the amount of distortion is increased due to the delayed versions of the signal adding at the receiver input with their own uncorrelated Rayleigh fading statistics. This fading can be caused by a transmitted signal bouncing off a tall building or other structure. This condition is typically referred to as multipath distortion or delay spread distortion. This type of distortion results in a frequency null or notch in the spectrum of the modulation that severely degrades the performance of the communication system.
Coherent detectors are typically used in digital communications for the symbol decision process. Coherent detection is described in Bernard Sklar, Digital Communications, Fundamentals and Applications, Chapter 3 (1988). In a delay spread distortion environment, however, a detector alone cannot remove the distortion caused by the same signal being received at multiple times. This type of detection requires a detector with a channel equalizer. A typical channel equalizer structure is the decision feedback equalizer (DFE). The DFE can phase track and cancel the distortion caused by the delayed version of the signal. Once the distortion is cancelled, the eight point constellation is generated at the detector output. DFEs are described in John Proakis, Digital Communications, Chapter 6 (1989). The channel equalizer, however, should not be used in an environment without delay spread distortion as it can cause sensitivity degradation compared to a coherent detector without the equalizer. There is a resulting need for a coherent detection algorithm that works equally well in an environment with and without delay spread distortion.